Brahimi was expected to assume his duties once Annan's resignation becomes official Aug. 31.
"Diplomacy to promote a peaceful resolution to the conflict in Syria remains a top priority for the United Nations," a U.N. spokesman said.
Annan, the former U.N. secretary-general, was appointed joint special envoy for the crisis in Syria in late February but the peace plan he offered was never implemented.
More than 17,000 people, mostly civilians, have been killed since the uprising against President Bashar Assad began some 17 months ago, the U.N. has estimated, and recent reports indicate the violence is escalating in Damascus and Aleppo, Syria's largest city.
The White House praised Brahimi's appointment, calling him a "capable and seasoned diplomat."
The U.N. Security Council Thursday voted to end the U.N. observer mission in Syria.
French U.N. Ambassador Gerard Araud, the council's president this month, said conditions for extending the observer mission had not been met.
Those conditions included halting Syria's escalating violence and convincing Assad's regime to stop using heavy weapons on civilian populations.
"If you don't renew the mandate, the mandate is over," Araud said.
The observer mission, whose mandate ends Sunday, will be dismantled starting in "a few days," Araud said. At its peak it had 300 unarmed observers.
Araud said the council approved a request by Secretary-General Ban Ki-moon to keep a small civilian office in Damascus to monitor events.
U.N. Assistant Secretary-General for Peacekeeping Operations Edmond Mulet, who attended the Security Council meeting and will help oversee the observers' withdrawal, said the office would probably have 20 to 30 staffers. Its precise duties were not yet defined, but they would not include military observation, he said.
The observer mission was created as part of a Syrian peace plan negotiated by Annan, who resigned Aug. 2 in frustration over his inability to persuade Assad and the opposition to halt the conflict, now in its 18th month.
Russian U.N. Ambassador Vitaly Churkin told reporters separately the five permanent Security Council members -- the United States, Britain, France, Russia and China -- and key regional players would meet on Syria in New York Friday.
Brahimi, a former Algerian foreign minister who has worked for the United Nations in other trouble spots, including Afghanistan and Iraq, is a member of The Elders, an independent group of noted world leaders and elder statesmen working for global peace and human rights. The group, brought together by former South African President and Nobel Peace laureate Nelson Mandela, is led by Nobel Peace laureate Archbishop Desmond Tutu.
Brahimi is a member of the Global Leadership Foundation, which promotes good governance around the world.
He is a distinguished senior fellow at the Center for the Study of Global Governance at the London School of Economics and Political Science and a governing board member of the Stockholm International Peace Research Institute.
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